Question

Solve the equation explicitly:
dx/dt - x^3 = x

Answer 1

I had to cheat to recall how to do some of this. The first part is to change this into a workable integral. We need the dt by itself:
\[\frac{dx}{dt}-x^3=x\]
\[\frac{dx}{dt}=x+x^3\]
\[\frac{dx}{x+x^3}=dt\]
Take the integral of both sides:
\[\int\limits dt= \int\limits (x+x^3)\]

Answer 2

http://www.wolframalpha.com/input/?i=integral+1%2F%28x%2Bx%5E3%29
See the show steps. I'm a little bit to rsuty to recall the specifics to type them out.

Answer 3

And that integral should be:
\[\int dt = \int (x+x^3)dx\]